The Independence Ratio of 4‐Cycle‐Free Planar Graphs

Key Points

• To establish the independence ratio for planar graphs with specific conditions related to cycles and triangles.
• Proving the independence ratio for planar graphs without triangles sharing edges with 4-cycles.
• Extending results to 4-cycle-free and planar graphs with adjacent triangles and specific cycles.
• The independence ratio for these graphs is established as a fixed value.
• Strengthened bounds were provided for planar graphs with no adjacent triangles and 5-cycles.